Question

solve for b and graph the solution. |b - 45| ≤ 25 click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them. submit

Explanation:

Step1: Solve the absolute - value inequality

Given \(|b - 45|\leq25\). By the definition of absolute - value inequality \(|x|\leq a\) (\(a\geq0\)) which is equivalent to \(-a\leq x\leq a\). Here \(x = b - 45\) and \(a = 25\). So we have \(-25\leq b-45\leq25\).
Add \(45\) to all parts of the compound inequality: \(-25 + 45\leq b-45 + 45\leq25+45\).
\(20\leq b\leq70\).

Step2: Graph the solution on the number - line

The solution \(20\leq b\leq70\) means that on the number - line, we have a line segment. The left - hand endpoint is at \(b = 20\) (a filled - in circle because \(b = 20\) is included in the solution set, since the inequality is \(\leq\)) and the right - hand endpoint is at \(b = 70\) (a filled - in circle because \(b = 70\) is included in the solution set).

Answer:

The solution of the inequality \(|b - 45|\leq25\) is \(20\leq b\leq70\). On the number - line, there is a line segment with endpoints at \(20\) (filled - in) and \(70\) (filled - in).